English

A formula for symmetry recursion operators from non-variational symmetries of partial differential equations

Mathematical Physics 2023-01-11 v3 math.MP

Abstract

An explicit formula to find symmetry recursion operators for partial differential equations (PDEs) is obtained from new results connecting variational integrating factors and non-variational symmetries. The formula is special case of a general formula that produces a pre-symplectic operator from a non-gradient adjoint-symmetry. These formulas are illustrated by several examples of linear PDEs and integrable nonlinear PDEs. Additionally, a classification of quasilinear second-order PDEs admitting a multiplicative symmetry recursion operator through the first formula is presented.

Keywords

Cite

@article{arxiv.2004.03743,
  title  = {A formula for symmetry recursion operators from non-variational symmetries of partial differential equations},
  author = {Stephen C. Anco and Bao Wang},
  journal= {arXiv preprint arXiv:2004.03743},
  year   = {2023}
}

Comments

26 pages; minor corrections and addition of example of Born-Infeld equation